Origin (mathematics)

This allows one to pick an origin point that makes the mathematics as simple as possible, often by taking advantage of some kind of geometric symmetry.

[1] The origin divides each of these axes into two halves, a positive and a negative semiaxis.

[1] In a polar coordinate system, the origin may also be called the pole.

It does not itself have well-defined polar coordinates, because the polar coordinates of a point include the angle made by the positive x-axis and the ray from the origin to the point, and this ray is not well-defined for the origin itself.

[3] In Euclidean geometry, the origin may be chosen freely as any convenient point of reference.